For positive integers $a$, $b$, and $c$,
$$a(b + c)$$
the expression equals an odd number.
Accordingly,
I. $a^{b} + c$\\
II. $b^{c} + a$\\
III. $c^{a} + b$
Which of these expressions always equals an odd number?
A) Only II\\
B) Only III\\
C) I and II\\
D) II and III\\
E) I, II, and III